Forecasting Financial Stress Indices in Korea: A Factor Model Approach

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Munich Personal RePEc Archive

Forecasting Financial Stress Indices in Korea: A Factor Model Approach

Kim, Hyeongwoo and Shi, Wen and Kim, Hyun Hak

Auburn University, Columbus State University, Kookmin University

October 2018

Online at https://mpra.ub.uni-muenchen.de/89768/

MPRA Paper No. 89768, posted 30 Oct 2018 00:43 UTC

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Forecasting Financial Stress Indices in Korea:

A Factor Model Approach

Hyeongwoo Kim Auburn University

Wen Shi

^y

Columbus State University Hyun Hak Kim

^z

Kookmin University October 2018

Abstract

We propose factor-based out-of-sample forecast models for Korea’s …nancial stress index and its 4 sub-indices that are developed by the Bank of Korea. We extract latent common factors by employing the method of the principal components for a panel of 198 monthly frequency macroeconomic data after di¤erencing them. We augment an autoregressive-type model of the …nancial stress index with estimated common factors to formulate out-of-sample forecasts of the index. Our models overall outperform both the stationary and the nonstationary benchmark models in forecasting the …nancial stress indices for up to 12-month forecast horizons. The …rst common factor that represents not only …nancial market but also real activity variables seems to play a dominantly important role in predicting the vulnerability in the …nancial markets in Korea.

Keywords: Financial Stress Index; Principal Component Analysis; PANIC; In-Sample Fit; Out-of-Sample Forecast; Diebold-Mariano-West Statistic

JEL Classi…cation: E44; E47; G01; G17

Patrick E. Molony Professor of Economics, Auburn University, 138 Miller Hall, Auburn, AL 36849. Tel:

+1-334-844-2928. Fax: +1-334-844-4615. Email: gmmkim@gmail.com.

yContact Author: Wen Shi, Department of Accounting & Finance, Turner College of Business, Colum- bus State University, Columbus, GA 31907. Tel: (706) 507-8155. Fax: (706) 568-2184. Email:

shi_wen@columbusstate.edu.

zDepartment of Economics, Kookmin University, Seongbuk-Gu, Seoul, Korea. Tel: +82-70-3787-3318.

Email: hyunhak.kim@kookmin.ac.kr.

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1 Introduction

The bankruptcy of Lehman Brothers on September 15, 2008 has triggered the collapse of

…nancial markets not only in the US but also in other countries including Korea. Since then, the Korean Won has depreciated against the US dollar by 18.2% in mere one quarter as global risk aversion spurred the demand for safe assets, leading to strong deteriorating spillover e¤ects on real sectors. Share prices fell by 15.3% and 25.4% in the last two quarters of 2008.¹

As we can see in this episode, …nancial market crises often occur abruptly, and quickly spread to other sectors of the economy, even to other countries. That is, …nancial market crises tend to come to a surprise realization with no systemic warnings. Since …nancial crises have harmful long-lasting spillover e¤ects on real activities even after the …nancial system becomes stabilized, it would be useful to have forecasting algorithms such as an Early Warning Signal (EWS), which can provide timely information on the vulnerability in

…nancial markets that might be materialized in the near future.

There’s an array of research works that attempt to predict …nancial crises in the current literature. For instance, Frankel and Saravelos [2012], Eichengreen et al. [1995], and Sachs et al. [1996] used linear regressions to test the statistical signi…cance of various economic variables on the occurrence of crises. Some others employed discrete choice model approaches, either parametric probit or logit regressions (Frankel and Rose [1996]; Cipollini and Kapetanios [2009]) or nonparametric signal detection approaches (Kaminsky et al. [1998];

Brüggemann and Linne [1999]; Edison [2003]; Berg and Pattillo [1999]; Bussiere and Mulder [1999]; Berg et al. [2005]; EI-Shagi et al. [2013]; Christensen and Li [2014]).

It is crucial to …nd a proper measure of …nancial market vulnerability, which quanti…es the potential risk that prevails in …nancial markets. One popularly used measure in the current literature is the Exchange Market Pressure (EMP) index. Since the seminal work of Girton and Roper [1977], many researchers have used the EMP index to develop EWS mechanisms in order to detect the turbulence in the money market across countries. See Tanner [2002] for a review.

One alternative measure that is rapidly gaining popularity is …nancial stress index (FSI).

Unlike the EMP index that is primarily based on changes in exchange rates and international reserves, FSI’s are typically constructed using a broad range of …nancial market variables. As of 2015, there are 12 FSIs available for the US …nancial market (Oet et al. [2011]) including 4 indices that are reported by the US Federal Reserve system.²

1Source: Organization for Economic Co-operation and Development, Total Share Prices for All Shares for the Republic of Korea [SPASTT01KRQ657N]

2For some of FSI’s in the Euro, see Grimaldi [2010], Grimaldi [2011], Hollo et al. [2012], and Islami

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Some recent studies investigate what economic variables help predict …nancial market vulnerability using FSI’s. For instance, Christensen and Li [2014] propose a model to forecast the FSIs developed by the IMF for 13 OECD countries, utilizing 12 economic leading indicators and three composite indicators. They used the signal extraction approach pro- posed by Kaminsky et al. [1998]. Slingenberg and de Haan [2011] constructed their own FSIs for 13 OECD countries and investigated what economic variables have predictive contents for the FSIs via linear regression models. Unfortunately, they fail to …nd any clear linkages between economic variables and those FSI’s.³

The present paper proposes a new forecasting model for the …nancial market vulnerability in Korea using a broad range of time series macroeconomic data. We use the …nancial stress index and its four sub-indices developed by the Bank of Korea.^4,5 We estimate multiple latent common factors by employing the method of the principal components (Stock and Watson [2002]) for a panel of 198 monthly frequency time series data from October 2000 to December 2013.⁶ We augment an autoregressive-type model of the …nancial stress index with estimated common factors, then formulate out-of-sample forecasts of the index for up to 12-month forecast horizons. We evaluate the out-of-sample forecast predictability of our models in comparison with two benchmark models, the nonstationary random walk (RW) and a stationary autoregressive (AR) model using the ratio of the root mean square prediction errors (RRM SP E) and the Diebold-Mariano-West (DM W) test statistics.

Note that these statistics are primarily based on the least squares (LS) principles, meaning that our major focus is to develop a good model that out-of-sample forecasts FSIs well on average. Alternatively, one may employ a tail-based performance metrics to …nd forecasting models that perform well in capturing a tail event, which occurs rarely by construction.

Although this type of models provide very useful information, we are more interested in developing simple prediction models in a data rich enviroment that are designed for constant monitoring to detect unusually high elevations in FSIs that ultimately can lead to a systemic

…nancial crisis.

and Kurz-Kim [2013]. There are FSI’s for individual countries: Greece (Louzis and Vouldis [2011]), Sweden (Sandahl et al. [2011]), Canada (Illing and Liu [2006]), Denmark (Hansen [2006]), Switzerland (Hanschel and Monnin [2005]), Germany (van Roye [2011]), Turkey(Cevik et al. [2013]), Colombia (Morales and Estrada [2010]), and Hong Kong (S.Yiu et al. [2010]).

3Misina and Tkacz [2009] investigated the predictability of credit and asset price movements for …nancial market stress in Canada. Kim and Shi [2015] implemented forecasting exercises for the FSI in the US using a similar methodologies used in this paper.

4The 4 sub-indices are for the foreign exchange market, the stock market, the bond market, and the

…nancial industry in Korea.

5The data is not publicly available and is for internal use only. We express our gratitude to give permission to use the data.

6We categorized these 198 variables into 13 groups that include an array of nominal and real activity variables.

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Our major …ndings are as follows. First, our factor models overall outperform the benchmark models. For example, in our exercise for the foreign exchange market sub-index, RRM SP E was substantially greater than one (smaller mean squared prediction errors of our models) and the DM W test rejects the null of equal predictability for majority cases from 1 to 12-month forecast horizons. Second, parsimonious models with just one single factor perform as well as bigger models that include up to 8 common factors. Augmenting the AR-type model of the FSI with the …rst common factor seems to be su¢cient to beat the benchmark models. Third, …xed-size rolling window methods performed overall similarly well as the recursive approach, which implies the stability of our models over time. We note that the …rst common factor, which plays a dominantly important role in predicting the FSIs, represents not only …nancial market but also real activity variables. That is, our

…ndings suggest that real sector variables also contain substantial predictive contents for the

…nancial market vulnerability in Korea.

We further investigate more speci…c channels of shocks by estimating macroeconomic factors separately from those from the monetary/…nance variables. Our out-of-sample forecast exercises reveal overall stronger performance of the full factor models especically for the total FSI, meaning that a wide range of macro-…nance variables contain useful predictive contents for the vulnerability in Korea’s …nancial market system. On the other hand, for FSI-bond and FSI-Stock, we show that our monetary/…nance factor models outperform not only the AR benchmark model but also the total factor model, which implies that the predictability for these indices can be improved by excluding the macroeconomic factors.

The rest of the paper is organized as follows. Section 2 describes the baseline econometric model and the out-of-sample forecasts schemes used in the present paper. We also explain our evaluation methods for our models. In Section 3, we provide data descriptions and preliminary analyses for latent common factor estimates. Section 4 reports our major …ndings from in-sample …t analyses and out-of-sample forecast exercises. In Section 5, we report forecast performances of our sub-factor models relative to the total factor model, and discuss the implications of the …ndings. Section 6 concludes.

2 The Econometric Model

Let xi;t be a macroeconomic variable i 2 f1;2; ::; Ng at time t 2 f1;2; ::; Tg. Assume that xi;t has the following factor structure.

xi;t =ci+ ⁰_iF_t+ei;t; (1)

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where ci is a …xed e¤ect intercept, F_t= [F1;t Fr;t]⁰ is an r 1vector of latent common factors, and i = [ i;1 i;r]⁰ denotes anr 1vector of factor loading coe¢cients for xi;t. ei;t is the idiosyncratic error term.

Estimation is carried out via the method of the principal components for the …rst- di¤erenced data. As Bai and Ng [2004] show, the principal component analysis estimators for F_t and i are consistent irrespective of the order of F_tas long asei;t is stationary. However, if ei;t is an integrated process, a regression of xi;t on F_t is spurious. To avoid this problem, we apply the method of the principal components after di¤erencing the data. Lag (1) by one period then subtract it from (1) to get,

xi;t = ⁰_i F_t+ ei;t (2)

fort= 2; ; T. Let x_i = [ xi;1 xi;T]⁰ and x= [ x₁ x_N]. We …rst normalize the data before the estimations, since the method of the principal components is not scale invariant. Employing the principal components method for x x⁰ yields factor estimates

F^_t along with their associated factor loading coe¢cient estimates ^

i. Estimates for the idiosyncratic components are naturally given by the residuals e^i;t = xi;t ^⁰

i F^_t. Level variables are then recovered by re-integrating these estimates,

^ ei;t =

Xt

s=2

^

ei;s (3)

for i= 1;2; :::; N. Similarly,

F^_t = Xt

s=2

F^_s (4)

After obtaining latent factor estimates, we augment an AR-type model for the …nancial stress index (f sit) with F^_t. Abstracting from deterministic terms,

f sit+j = _j⁰ F^_t+ jf sit+ut+j; j = 1;2; ::; k (5) That is, we implement direct forecasting regressions for the j-period ahead …nancial stress index (f sit+j) on (di¤erenced) common factor estimates ( F^_t) and the current value of the index (f sit), which belong to the information set ( t) at timet.⁷ Note that (5) is an AR(1) process for j = 1, extended by exogenous common factor estimates F^_t. This formulation is based on our preliminary unit-root test results for the FSI’s that show strong evidence of

7Alternatively, one may use arecursive forecasting regression model that replaces j with ^j, where is the coe¢cient from an AR(1) model.

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stationarity.⁸ Applying the ordinary least squares (OLS) estimation for (5), we obtain the following j-period ahead forecast for the …nancial stress index.

f sic^F_t+jjt= ^⁰

j F^_t+ ^jf sit (6)

To statistically evaluate our factor models, we employ the followingnonstationaryrandom walk (RW) model as a (no change) benchmark model.

f sit+1 =f sit+"t+1 (7) It is straightforward to show that (7) yields the followingj-period ahead forecast.

f sic^RW_t+jjt =f sit; (8)

where f sit is the current value of the …nancial stress index.

In addition to the RW model, we also employ the following stationary AR(1) model as the second benchmark model.

f sit+j = jf sit+"t+1; (9) where j is the coe¢cient on the current FSI in the direct regression for the j-period ahead FSI variable. This model speci…cation yields the following j-period ahead forecast.

f sic^AR_t+jjt = ^jf sit; (10)

where ^j is the least squares estimate for j.

For evaluations of the prediction accuracy of our models, we use the ratio of the root mean squared prediction error (RRM SP E), that is, RM SP E from the benchmark model divided by RM SP E from the factor model. Note that our factor model outperforms the benchmark model whenRRM SP E is greater than 1.

Also, we employ the Diebold-Mariano-West (DM W) test for further statistical evaluations of our models. For the DM W test, we de…ne the following loss di¤erential function.

dt=L("^A_t+jjt) L("^F_t+jjt); (11) where L( )is a loss function from forecast errors under each model, that is,

"^A_t+jjt =f sit+j f sic^A_t+jjt (A=RW; AR); "^F_t+jjt=f sit+j f sic^F_t+jjt (12)

8ADF test results are available upon request.

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One may use either the squared error loss function, ("^j_t+jjt)², or the absolute loss function, j"^j_t₊_jjtj.

The DM W test statistic tests the null of equal predictive accuracy,H0 :Edt= 0, and is de…ned as follows.

DM W = d

qAvar(d)[

; (13)

where d is the sample mean loss di¤erential, d = _T ¹_T₀ PT

t=T0+1dt, and Avar(d)[ denotes the asymptotic variance of d,

Avar(d) =[ 1 T T0

Xq

i= q

k(i; q)^

i (14)

k( )is a kernel function where T0=T is the split point in percent,k( ) = 0; j > q, and ^_j is j^th autocovariance function estimate.⁹ Note that our factor model (5) nests the stationary benchmark model in (9) with j=0. Therefore, we use critical values obtained with re- centered distributions of the test statistic for nested models (McCracken [2007]). For the DM W statistic with the random walk benchmark (7), which is not nested by (5), we use the asymptotic critical values, which are obtained from the standard normal distribution.

3 Data Descriptions and Factor Estimations

3.1 Data Descriptions

We use the …nancial stress index (FSI) data to assess the degree of the vulnerability in

…nancial markets in Korea to potential risk of having possible …nancial crises. Financial Condition Indices (FCI) share similar information as FSI’s in the sense that they all measure the current …nancial conditions in the economy, though FCI’s focus more on how …nancial variables react to changes in the market conditions.

There were earlier attempts to develop an FSI by the Bank of Canada in 2003 and the Swiss National Bank in 2004, while the Kansas City Fed and the St. Louis Fed in the U.S.

also began using FSIs since 2008. In Korea, the Bank of Korea developed FSIs in 2007 and started to report the indices on a yearly basis in their Financial Stability Report. We obtained monthly frequency data which have been transformed from daily frequency raw data. The data are in principle for internal use only.¹⁰

The Korea’s FSI data is based on 4 sub-indices for the bond market (FSI-Bond), the

9Following Andrews and Monahan [1992], we use the quadratic spectral kernel with automatic bandwidth selection for our analysis.

10We obtained permission from the Bank of Korea to use the data for this research.

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foreign exchange market (FSI-FX), the stock market (FSI-Stock), and the …nancial industry (FSI-Industry). Each sub-index is constructed as follows. FSI-Bond is based on a variety of credit spreads, long-short interest rate spreads, and covered interest rate di¤erentials (CID).

FSI-FX is obtained by utilizing the volatility and the growth rate of the Korean Won-US Dollar exchange rate as well as the growth rate of Korea’s foreign exchange reserves. FSI- Stock is constructed based on the volatility and the growth rate of KOSPI (Korea Composite Stock Price Index), and the volatility and growth rate of the KOSPI trade volume. Lastly, FSI-Industry is based on the volatility and the s of …nancial intermediaries’ stocks, and the spread between the average bond yields issued by …nancial intermediaries and the treasury bond yield.

As we can see in Figure 1, all sub-indices show overall similar movements as the total FSI index. FSI-Bond exhibits much lower volatility than FSI, while FSI-Stock shows the highest volatility. All indices imply extremely high degree vulnerability during the recent …nancial crisis that began in 2008.

Note that these indices keep track of actual historic events of …nancial crises, including the burst of the dot com bubble and the recent …nancial crisis, which con…rms that the Bank of Korea’s FSIs may provide useful timely signals of rising tensions in Korea’s …nancial market system. Given that, developing a good forecasting model for these FSIs would provide useful information to the policy makers.

Figure 1 around here

We obtained all macroeconomic time series data from Kim [2013], which are used to extract latent common factors for our out-of-sample forecast exercises. Observations are monthly frequency and span from October 2000 to December 2013. All variables other than those in percent (e.g., interest rates and unemployment rates) are log-transformed prior to estimations. We categorized 198 time series data into 13 groups as summarized in Table 1.

Group #1 that includes 14 time series data represents a set of nominal interest rates.

Groups #2 through #4 include prices and monetary aggregate variables, while group #5 covers an array of bilateral nominal exchange rates. Note that these groups overall represent the nominal monetary/…nance sector variables. On the contrary, group #6 through

#11 entail various kinds of real activity variables such as manufacturers’ new orders, inventory, capacity utilizations, and industrial production indices. The last two groups represent business condition indices and stock indices in Korea, respectively.

Table 1 around here

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3.2 Latent Factors and their Characteristics

We estimate up to 8 latent common factors by applying the method of the principal components (PCA) to 198 macroeconomic data series after di¤erencing and normalizing them.

Estimated (di¤erenced) common factors, F^1; F^2; :::; F^8; as well as their associatedlevel common factor estimates F^1;F^2; :::;F^8, obtained by re-integrating di¤erenced common factors, in the Appendix.

We note a dramatic decline in the …rst common factor estimate F^1 around the beginning of the Great Recession in 2008. Similarly, the second common factor estimates F^2 exhibits an abrupt downward movement about the same time. All estimated common factors inlevels exhibit highly persistent dynamics, indicating a nonstationary stochastic process. Therefore, it seems to be appropriate to employ PCA to the data after di¤erencing them to ensure the stationarity of the data (see Bai and Ng [2004]) to consistently estimate the factors.

To understand the source of each latent factor more closely, we estimate the factor loading coe¢cients (^

i). In addition, we provide the marginalR²analysis by regressing each predictor variable xi;t on each common factor estimate F^i to get R² values. All results are reported in the Appendix.

In what follows, we investigate the properties of the three key common factors to under- stnad the nature of those factors. First, we plot F^1 and F^1 as well as its associated factor loading coe¢cients (^

i;1) and the marginal R² values in Figure 2.

We note that the factor loading coe¢cients for the …rst four groups (groups #1 through

#4) and the last three groups (groups #11 through #13) are positively associated with F^1, while variables in groups #5, #6, and #8 are mostly negatively associated with it.

Overall, F^1represents not only the monetary variables (e.g., interest rates, prices, monetary aggregates, and nominal exchange rates) but also real activity macroeconomic variables (e.g., new orders, industrial production, and industrial production).

Factor loading coe¢cients imply positive associations between Interest rates and prices (in‡ation rates), which seems to be consistent with the Fisher E¤ect. Domestic prices are negatively related with nominal exchange rates (relative prices of the domestic currency), because domestic in‡ation is likely to be associated with depreciation of the home currrency.

Marginal R² analysis results are overall consistent with the factor loading coe¢cients. To put it di¤erently, F^1 seems to be representing both the monetary variables (#1, #2, #3,

#5) and the macroeconomic variables (#11, #12, #13).

As we can see in Figure 3, the second common factor seems to closely represent variables

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in groups #5, #6, and #9 through #12, which are real sector variables with an exception of group #5. F^2is overall positively related with the majority of the variables in these groups.

For instance, the factor loading coe¢cients (^

i;2) for nominal exchange rates (group #5) are positive, which implies that a depreciation of Korean wons ( xi;t > 0) are associated with an increase in real activities ( F^2 >0) in Korea, that is, ^

i;2 F^2 >0. Similarly, new orders, sales, industrial production, and business condition index variables have positive coe¢cients.

Among the variables in group #10, unemployment variables have negative coe¢cients, while employment variables tend to exhibit positive ones, which are consistent with each other.

Putting all together, F^2 seems to represent overall real sector variables.

In what follows, our in-sample-…t analysis demonstrates a substantially important role of the fourth common factor estimate F^4 in explaining FSIs. So we investigate the properties of F^4 more closely in Figure 4. Estimates of i;4 imply that F^4 is more closely related with monetary/…nance variables in groups #1 through #5, while some variables among macroeconomic variable groups #7 and #8 (inventory indices) are also somewhat closely related with F^4. The marginalR² analysis also con…rms these …ndings. Therefore, we may conclude F^4 primarily represents the nominal/monetary variables.

4 Forecasting Exercises

4.1 In-Sample Fit Analysis

We implement an array of least squares estimations for the following equation, employing alternative combinations of estimated common factors n

F^1; F^2; :::; F^8

o

as predictor variables.

f sit+j = _j⁰ F^_t+ut+j; j = 0;1;2; ::; k (15) We report our in-sample …t analyses in Table 2 for the contemporaneous case (j = 0).¹¹

We employed an R²-based selection method from a one-factor model to an eight-factor full model to …nd the best combination of explanatory variables. It turns out that the …rst

11Regressions for the 1-, 3-, and 6-month ahead FSI indices yield similar patterns, although R² values overall decline as the time horizon becomes larger.

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common factor estimate F^1 plays the most important role in explaining variations in all FSI indices with an exception of FSI-Bond. The second common factor estimate F^2 explains a negligibly small portion of variations in FSI indices.

Since R² increases as more variables are included, thisR²-based selection method always picks the full model as the best one. So, we considered two alternative selection methods.

The adjustedR² selection method chose a 7-factor model, while a step-wise selection method (Speci…c-to-General rule) picked a 6-factor model for FSI and a 5-factor model for FSI-FX.

It should be noted, however, that maginal gains from adding more factors are often small, which implies that small dimension models with just one or two factors are su¢cient to obtain a good in-sample …t for each …nancial stress index. In what follows, we demonstrate that parsimonious models perform well in out-of-sample forecast exercises as well.

Table 2 around here

We also implement similar in-sample analysis based on (15) for the time horizon j = 0;1; :::;12 months. R² values for FSIs are reported in Figure 5. We note that the …rst common factor ( F^1) explains the most variations not just in contemporaneous FSIs (over 20%) but also in up to a half-year (h = 0;1;2; :::;6) ahead FSIs with an exception of FSI- bond. It is interesting to see that F^4 overall plays a non-negligible role especially in the short-run. For example, its R² values for contemporaneous FSI and FSI-Stock exceeded 0.10. Recall that F^4 represents mainly monetary variables that include interest rates and exchange rates. That is, these fast-moving variables provide more predictive contents through F^4 in addition to those in F^1 that represents both the monetary and the slow-moving macroeconomic variables. Other than these two factors, none explains much of the variations in FSIs, although F^7 contains some predictive contents in the medium-run.

4.2 Out-of-Sample Forecast Exercises and Model Evaluations

We implement out-of-sample forecast exercises using the following two schemes. First, we employ a recursive forecast method. We start formulating k period ahead out-of-sample forecasts of FSI’s (f siT0+k) using the initial T0 observations.¹² That is, we extract common

12We used 70% initial observations.

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factors fromfxi;tg^t_i=1;::;N⁼¹^;:::;T⁰ after di¤erencing. Then, we formulate our factor model forecast via (6). Next, we add one new set of observations to the sample and implement next forecast for f siT0+1+k using this expanded set of observations fxi;tg^t=1;:::;T_i₌₁_;::;N⁰⁺¹. We repeat this procedure until we forecast the last observation f siT. We implement this scheme for up to 12-month forecast horizons, j = 1;3;6;9;12.

The second scheme is a …xed-size rolling window method that repeats forecasting by adding one additional observation with the same split point (T0=T) but dropping one earliest observation, maintaining the same sample size.

For statistical evaluations of our factor model, we employ the two benchmark models, the random walk (RW, no change) model and a stationary AR(1) model, and formulate forecasts via the equations (8) and (10), respectively. We evaluate our factor model forecasting performances relative to these benchmark models using the following two popular measures.

First, we report the ratio of the root mean square prediction error, RRM SP E, of each of the benchmark models relative to that of our factor models. Note that the factor model outperforms the benchmark model when the RRM SP E is greater than one. Second, we employ the DM W statistics with asymptotic critical values when the random walk model is used, while the critical values from McCracken [2007] were used when the AR model is used because the AR model is nested by our factor models.

Our forecast exercise results for the total FSI are reported in Table 3. To save space, we report results with three 1-factor models, two two-factor models, and one three-factor model, which are chosen based on our in-sample …t analyses in previous section.

We note that our factor models outperform the RW model for all forecast horizons from 1-month to 1-year. RRM SP E is greater than one for all cases, denoted in bold. Our factor models outperform the benchmark model with theDM W test for majority cases. For example, theDM W test rejects the null of equal predictability at the 10% signi…cance level for 24 out of 30 cases both with the recursive method and the rolling window method. We

…nd especially strong out-of-sample forecast performances when the forecast horizon is equal to or greater than 3 months.

It turns out that our factor models also perform reasonably well in comparison with the stationary AR(1) benchmark model. RRM SP E is greater than one for majority cases when the recursive method is employed, whereas our models perform relatively poorly when the rolling window method is used. Interestingly, the 1-factor model with F^4, which is more closely related with nominal monetary variables, performs consistently poorly. We note that the DM W test rejects the null of equal predictability for 7 out of 12 one-period ahead forecasts, whileRRM SP E is greater than 1 (in bold) for 10 out of 12 cases. This is a good property because out-of-sample forecast exercises are more useful when it demonstrates

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superior predictability for short forecast horizon, as …nancial turmoils often occur suddenly without systematic warnings.

Table 3 around here

Table 4 reports out-of-sample forecast exercise results for FSI-Bond. Irrespective of its poor in-sample …t as seen in previous section, our factor model beats the RW model again for most cases byRRM SP E criteria. TheDM W test rejects the null of equal predictability for most cases whenj = 3;6;9;12at least at the10%signi…cance level. With the AR model as the benchmark, our factor models overall perform well especially when j = 3;6;9;12.

Recall that F^4 explains the most of variations, although small, in FSI-Bond as can be seen in Table 2. It is interesting to see that F^4 exhibit the best out-of-sample predictability even when all other models perform poorly in comparison with the AR model. In what follows, we show that forecast models that utilize factors only from the monetary/…nance variables outperform the AR benchmark by both the RRM SP E and the DM W statistics criteria, indicating that the predictability can be enhanced by excluding the macroeconomic variables.

Table 4 around here

Our factor models perform overall extememly well for FSI-FX, especially when the rolling window method is employed. RRM SP E is greater than one for all cases with the random walk benchmark model, while the DM W test rejects the null for all cases when the rolling window scheme is employed. Our models exhibit failry good one-period ahead forecast performances with the AR benchmark whenever F^1 is used.

Table 5 around here

Out-of-sample forecast performances for FSI-Stock are reported in Table 6. RRM SP E is greater than 1 in most cases with the RW benchmark model, while theDM W test rejects the null of equal predictability only when j = 12. With the AR model, factor models demonstrated limited success in a few cases, though theDM W test rejects the null for 5 out of 6 cases when the rolling window scheme is used for one-period ahead forecasts. Similar to the case of FSI-Bond, we show that the predictability can be enhanced when factors are extracted only from the monetary/…nance variables in the next section.

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Table 6 around here

Finally, we report forecast exercise results for FSI-Industry in Table 7. Our factor models performed better than the random walk model only when the forecast horizon is longer than a half year. RRM SP E was often less than one when j = 1;3. Forecast performances were worse especially when the AR model serves as the benchmark. Overall, our factor models perform the worst for FSI-Industry, although F^4 seems to perform relatively better than other factors.

Table 7 around here

5 Discussions

5.1 Macroeconomic vs. Monetary Variables

This section extracts common factors from two groups of predictor variables: monetary/…nance variables (groups #1 through #5) and macroeconomic variables (groups #6 through #13).

Since the latent factors are estimated from a large panel of time series, they contain not only fast-moving monetary variables but also slow-moving macro variables. The idea is to evaluate the individual roles of the macroeconomic and …nance factors by estimating common factors from these groups of variables separately.

We …rst investigate how common factors from the entire predictor variables ( Fî) are associated with common factors from the monetary variables ( M nFî) and those from the macroeconomic variables ( M cFî). Scatter plot diagrams in Figure 6 con…rm our earlier conjectures about the source of each common factor ( Fî). F^1 is closely associated with the

…rst factor from the monetary variables M nF1 as well as the two factors from the macroeconomic variables, M cF1 and M cF2 in the sense that the slope coe¢cient estimates ( ) were highly signi…cant at the 5% signi…cance level. F^2 seems to be mainly extracted from macroeconomic variables. On the other hand, the major source of F^4 seems to be the monetary/…nance variables because it is strongly correlated with M nF1 and M nF2, while the estimate for F^4 and M cF2 is only marginally signi…cant.

We report out-of-sample predictability test results for the macro and …nancial factors in Tables 8 through 12. For the total FSI, it seems that the full factor models perform better

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than the sub-factor models, the macro and the …nance factors, in terms of signi…cance of the DM W test. See Tables 3 and 8. For both the rolling window and recursive schemes and for the both benchmark models, F^i exhbited superior performances to M nFi and M cFi, although M nF1 peformed overall better than the macro factors.

Table 8 around here

The full factor model for FSI-Bond again perform better than the sub-factor models in terms of signi…cance of the DM W test. See Tables 4 and 9. Interestingly, the …nance factors outperform the macro factors in the tests with the AR benchmark model. M nFi

exhibited a superior predictability both in terms of theRRM SP E and theDM W statistics, while the AR benchmark model performed better than M cFi. Recall that the total factor model did not beat the AR benchmark (Table 4). These …ndings imply that major gains in out-of-sample predictability of the full factor model are obtained from the monetary/…nance predictor variables, and its predictability can be improved by excluding the macroeconomic variables.

Table 9 around here

These …ndings for FSI-Bond contrast sharply with those for FSI-FX. See Tables 5 and 10.

The full factor model again outperforms the sub-factor models. However, unlike the previous results for FSI-Bond, the macro factors perform better than monetary factors in the tests with the AR benchmark model, although M cFi contained good prediction contents only for 1-month (j = 1) and 1-year (j = 12) ahead FSI-FX. That is, it seems that the predictability of the full factor model mainly comes from the macro predictor variables, which sharply contrasts with the case of FSI-Bond.

Table 10 around here

Our forecasting exercises for FSI-Stock with the sub-factor models exhibit intriguing results that the …nance factor models outperform the full factor models in terms ofRRM SP E and theDM W test statistics. See Table 11. The DMW test mostly failed to reject the equal predictability null hypothesis for the full factor models (see Table 6), while the test rejected the null hypothesis for the monetary/…nance factor models whichever benchmark models were employed. That is, as in the case of FSI-Bond, our factor models perform better when we extract common factors only from the monetary variables.

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Lastly, the total factor models perform similarly well for FSI-Industry in comparison with the sub-factor models in the tests with the RW benchmark. However, the macro and …nance factor models barely outperform the AR benchmark, while M nF1 has a limited success in outperforming the AR model. We note that the full factor model performed relatively well against the AR model only when it contains F4 which extracts the predictive contents mostly from the monetary/…nance variables, which are consistent with the …ndings in Table 12.

Since Korea is a small open economy, its …nancial system may be vulnerable to spillover e¤ecfts of external shocks that originate from foreign large economies. This implies that common factors that are estimated from open economy variables may have useful predictive contents for the vulnerability of Korea’s …nancial system.

To assess this possibility, we estimate latent factors utilizing the following 50 open economy variables: 22 Morgan Stanley Capital International (MSCI) stock indices in the developed market category; 12 Korean stock market indices; 16 monentary variables including the VIX, 12 Korean won exchange rates, and 3 international interest rates.¹³ To save space, we report out-of-sample forecast exercises using only the one-factor model for all 5 FSIs in Table 13.

Results imply that this open economy sub-factor model performs as good as the total factor model only for FSI-FX when the RW model serves the benchmark. With the AR benchmark, the total factor model outperformed the open economy sub-factor model for all FSIs, implying that open economy factors have some useful but limited predictive contents for the stability in Korea’s …nancial system.

13Note that some variables such as Korean stock indices and bilateral exchange rates were included in our baseline study.

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5.2 Predictability of Sub-Indices

We compare the out-of-sample predictability of our factor model (5) against the following model with the four sub-indices. Abstracting from deterministic terms,

f sit+j = _j⁰sfsi_t+ut+j; j = 1;2; ::; k; (16) where f sit+j is the total …nancial stress index at time t+j and sfsi_t is a 4 1 vector of four sub-indices at timet. The idea is to check whether these sub-indices contain good out- of-sample predictive contents for the total FSI index, because it is a weighted average of the four sub-indices. Note that the lagged total index f sit cannot be included in the regression because it is not independent of sfsi_t. We report results in Table 14.

Our factor model completely outperforms this sub-indices benchmark model. AllRRM SP E values are greater than one, and the DM W test rejects the null of equal predictability at least at the 5% signi…cance level, meaning that our factor-based forecasting models extract additional important predictive contents for f sit+j that are not contained in the four sub- indices.

5.3 Time-Varying Coe¢cient?

Our out-of-sample forecast exercises require repeated estimations of common factors using either a recursive or a …xed-size rolling window scheme. One related question is whether we estimate the same underlying factors consistently from these repeated estimations because of the "latent nature" of common factors. Therefore, it might be an interesting exercise to see how factor estimates are formulated from the data over time, and whether the pattern of the dependency of factor estimates on each variabel remains stable over time.

For this purpose, we repeatedly estimate common factors using the following two methods. First method begins with estimating the common factors F_T

0 using the …rst T0

observations f xi;sg^s_i₌₁⁼¹_;:::;N^;:::;T⁰. Then, we implement the marginal R² analysis by regressing each variable in f xi;sg^s_i=1;:::;N⁼¹^;:::;T⁰ on F_T

0, which generates N marginal R² values. Then, we move the sample window to the right by one set of observations, f xi;sg^s_i=1;:::;N⁼²^;:::;T⁰⁺¹, and estimate the next set of the common factors F_T

0+1. Then, we obtain another N marginal R² values by the same regression method. We repeat until we obtain (T T0+ 1)sets of N marginal R² values.

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The second method estimates the common factors F_T using the entire T observations f xi;sg^s_i=1;:::;N⁼¹^;:::;T. Then, we implement the marginal R² analysis by regressing each of f xi;sg^s=1;:::;T_i₌₁_;:::;N⁰ on f F_T;sg_s₌₁_;:::;T₀. We shift the sample window by one and implement the same analysis utilizingf xi;sg^s=2;:::;T_i₌₁_;:::;N⁰⁺¹andf F_T;sg_s₌₂_;:::;T₀₊₁to get the next set of marginal R² values. We repeat until we obtain (T T0+ 1) sets ofN marginal R² values.

We report results for the …rst common factor in Figure 7. We note that marginal R² values from the both methods are similar with each other, although those from the rolling window scheme tend to be noisier. This implies that the data generating process of the

…rst latent common factor remains stable. F^1 has been closely associated with both the macroeconomic and the monetary/…nance variables. It is interesting to see marginal R² values have increased for some monetary variables, especially for bilateral exchange rates over time.

6 Concluding Remarks

This paper proposes an out-of-sample forecast model for the …nancial stress index developed by the Bank of Korea (BOK). We use the BOK’s highly con…dential …nancial stress index and its 4 sub-indices to measure the vulnerability in …nancial markets in Korea. To deal with issues on high data dimensionality, we employ a parsimonious method to extract latent common factors from a panel of 198 time series macroeconomic variables that includes not only nominal but also real activity variables. Following Bai and Ng [2004], we apply the method of the principal components to these variables after di¤erencing them to estimate the common factors consistently. Our in-sample …t analyses demonstrate that estimated factors explain substantial shares of variations of all …nancial stress indices with an exception of FSI-Bond.

We implement out-of-sample forecast exercises using the recursive and the …xed size rolling window schemes with the two benchmark models, the random walk and a stationary AR(1) models. We evaluate out-of-sample predictability of our factor models using the ratio of root mean square prediction errors (RRM SP E) and the DM W test statistics.

Our …ndings imply that there exists a tight linkage between the Korean FSI’s and estimated common factors. Interestingly, we observe that not only nominal but also real activity variables, proxied especially by the …rst common factor estimate, seem to contain

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useful predictive contents for FSIs in Korea. Especially, our factor models demonstrate superior performance over the random walk benchmark model in most cases. Our models also show fairly good performances relative to the AR model in short forecast horizons, which can be practically useful because …nancial crises often occur abruptly. We also …nd parsimonious models that are based on a few common factors perform as well as other bigger models.

We further delve into this matter by estimating common factors from the two sub-groups separately, the monetary/…nance variables and the macroeconomic variables. Although these sub-factor models overall perform well relative to the two benchmark models, the full factor models still outperform the sub-factor models for the total FSI. However, we note that the predictability for FSI-Bond and FSI-Stock can be enhanced greatly against the AR model when we utilize only the monetary/…nance factors excluding macroeconomic factors. That is, a broad range of variables seems to be useful to capture the vulnerability of Korea’s entire …nancial system, but bond and stock markets seem to be more greatly in‡uenced by fast-moving monetary/…nancial variables.

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Figure 1. Financial Stress Index (Dashed) and 4 Sub-Indices

Note: The total financial stress index and its four sub-indices are obtained from the Bank of Korea. The data is not publicly available but we obtained a permission to use them.

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Figure 2. Common Factor #1 and its Factor Loading Coefficients

Note: We estimate the latent common factors by employing the method of the principal components for a panel of 198 monthly frequency time series data after differencing the data to consistently estimate the factors given nonstationarity of the data. Level factors are recovered by re-integrating the differenced factor estimates. Marginal R² values were obtained via a regression of each predictor variablexi,t onto the common factor.

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Figure 5. Marginal R² for h-Period Ahead FSIs

Note: Marginal R² values were obtained via a regression of each common factor onto the j- period ahead financial stress index. We considered up to one year (j= 12) time hirozon.

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Figure 6. Macro and Monetary Common Factors

Note: ∆Fi,∆M nFi, and∆M cFi denote the common factor estimates from the entire variables, the monetary/finance variables (#1˜#5), and the macroeconomic variables (#6˜#13), respectively. β is the slope coefficient estimate and the standard errors are in the brackets.

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Figure 7. Robustness of Factor Estimates

(a) ∆ ˆF₁ from the Rolling Window Scheme (b) ∆ ˆF₁ from the Entire Observations

Note: Panel (a) reports marginalR²values utilizing the predictor variables and the first common factor estimate with a fixed-size rolling window. For this, we repeatedly re-estimate the first common factor. Panel (b) reports marginal R² values that are obtained the pre-estimated common factor and predictor variables with a fixed-size rolling window. That is, we first estimate the common factor using the entire observations, then apply the least squares regression with a rolling window scheme to obtain theR² values.

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Table 1. Macroeconomic Data Descriptions

Group ID Data ID Data Descriptions

#1 1-14 Domestic and World Interest Rates

#2 15-35 Exports/Imports Prices

#3 36-54 Producer/Consumer/Housing Prices

#4 55-71 Monetary Aggregates

#5 72-83 Bilateral Exchange Rates

#6 84-110 Manufacturers’/Construction New Orders

#7 111-117 Manufacturers’ Inventory Indices

#8 118-135 Housing Inventories

#9 136-157 Sales and Capacity Utilizations

#10 158-171 Unemployment/Employment/Labor Force Participation

#11 172-180 Industrial Production Indices

#12 181-186 Business Condition Indices

#13 187-198 Stock Indices

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Table 2. In-Sample Fit Analysis for Selection of Factors

Financial Stress Index

#Factors Factors R²

1 ∆ ˆF1 0.233

2 ∆ ˆF1, ∆ ˆF4 0.331

3 ∆ ˆF1, ∆ ˆF4, ∆ ˆF5 0.365

4 ∆ ˆF1, ∆ ˆF4, ∆ ˆF5, ∆ ˆF8 0.388

5 ∆ ˆF1, ∆ ˆF4, ∆ ˆF5, ∆ ˆF7, ∆ ˆF8 0.409 6^† ∆ ˆF1, ∆ ˆF2, ∆ ˆF4, ∆ ˆF5, ∆ ˆF7, ∆ ˆF8 0.421 7^∗ ∆ ˆF1, ∆ ˆF2, ∆ ˆF3, ∆ ˆF4, ∆ ˆF5, ∆ ˆF7, ∆ ˆF8 0.426 8 ∆ ˆF1, ∆ ˆF2, ∆ ˆF3, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.429

Financial Stress Index - Bond

1 ∆ ˆF4 0.036

2 ∆ ˆF4, ∆ ˆF5 0.054

3^† ∆ ˆF1, ∆ ˆF4, ∆ ˆF5 0.068

4^∗ ∆ ˆF1, ∆ ˆF4, ∆ ˆF5, ∆ ˆF8 0.079 5 ∆ ˆF1, ∆ ˆF2, ∆ ˆF4, ∆ ˆF5, ∆ ˆF8 0.083 6 ∆ ˆF1, ∆ ˆF2, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF8 0.084 7 ∆ ˆF1, ∆ ˆF2, ∆ ˆF3, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF8 0.085 8 ∆ ˆF1, ∆ ˆF2, ∆ ˆF3, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.085

Financial Stress Index: Foreign Exchange

1 ∆ ˆF1 0.324

2 ∆ ˆF1, ∆ ˆF4 0.373

3 ∆ ˆF1, ∆ ˆF4, ∆ ˆF7 0.395

4 ∆ ˆF1, ∆ ˆF4, ∆ ˆF6, ∆ ˆF7 0.405

5^∗† ∆ ˆF1, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7 0.414 6 ∆ ˆF1, ∆ ˆF2, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7 0.417 7 ∆ ˆF1, ∆ ˆF2, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.419 8 ∆ ˆF1, ∆ ˆF2, ∆ ˆF3, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.419 Note: ∗and† denote the chosen model by the adjustedR² method and the specific to general rule, respectively.

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Table 2. Continued

Financial Stress Index: Stock

1 ∆ ˆF1 0.235

2 ∆ ˆF1, ∆ ˆF4 0.357

3 ∆ ˆF1, ∆ ˆF4, ∆ ˆF8 0.388

4 ∆ ˆF1, ∆ ˆF4, ∆ ˆF7, ∆ ˆF8 0.417

5 ∆ ˆF1, ∆ ˆF4, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.438 6 ∆ ˆF1, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.456 7 ∆ ˆF1, ∆ ˆF2, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.471 8^∗† ∆ ˆF1, ∆ ˆF2, ∆ ˆF3, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.479

Financial Stress Index: Financial Industry

1 ∆ ˆF1 0.189

2 ∆ ˆF1, ∆ ˆF4 0.260

3 ∆ ˆF1, ∆ ˆF4, ∆ ˆF5 0.322

4 ∆ ˆF1, ∆ ˆF4, ∆ ˆF5, ∆ ˆF7 0.352

5 ∆ ˆF1, ∆ ˆF4, ∆ ˆF5, ∆ ˆF7, ∆ ˆF8 0.378 6 ∆ ˆF1, ∆ ˆF2, ∆ ˆF4, ∆ ˆF5, ∆ ˆF7, ∆ ˆF8 0.395 7 ∆ ˆF1, ∆ ˆF2, ∆ ˆF3, ∆ ˆF4, ∆ ˆF5, ∆ ˆF7, ∆ ˆF8 0.410 8^∗† ∆ ˆF1, ∆ ˆF2, ∆ ˆF3, ∆ ˆF4, ∆ ˆF5, ∆ ˆF6, ∆ ˆF7, ∆ ˆF8 0.421 Note: ∗and† denote the chosen model by the adjustedR² method and the specific to general rule, respectively.

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Table 3. j-Period Ahead Out-of-Sample Forecast: FSI

Recursive Method: Random Walk Benchmark

Factors j= 1 j= 3 j= 6 j= 9 j= 12

∆ ˆF1 1.040 1.097^† 1.251^‡ 1.344^‡ 1.398^‡

∆ ˆF4 1.031 1.084^† 1.217^† 1.296^‡ 1.415^‡

∆ ˆF5 1.049^† 1.128^† 1.246^† 1.331^‡ 1.392^‡

∆ ˆF1, ∆ ˆF4 1.039 1.076^∗ 1.235^† 1.302^‡ 1.416^‡

∆ ˆF1, ∆ ˆF5 1.049 1.100^∗ 1.279^‡ 1.357^‡ 1.397^‡

∆ ˆF1, ∆ ˆF4, ∆ ˆF5 1.047 1.079 1.270^† 1.315^‡ 1.413^‡ Rolling Window Method: Random Walk Benchmark

Factors j= 1 j= 3 j= 6 j= 9 j = 12

∆ ˆF1 1.050 1.106^† 1.280^‡ 1.378^‡ 1.438^‡

∆ ˆF4 1.021 1.085^∗ 1.219^† 1.354^‡ 1.432^‡

∆ ˆF5 1.039^∗ 1.111^† 1.279^† 1.348^‡ 1.442^‡

∆ ˆF1, ∆ ˆF4 1.036 1.084^† 1.244^‡ 1.371^‡ 1.437^‡

∆ ˆF1, ∆ ˆF5 1.057 1.090^∗ 1.331^‡ 1.374^‡ 1.437^‡

∆ ˆF1, ∆ ˆF4, ∆ ˆF5 1.043 1.071 1.295^‡ 1.377^‡ 1.435^‡ Recursive Method: Autoregressive Benchmark

Factors j= 1 j= 3 j= 6 j= 9 j= 12

∆ ˆF1 1.008 0.975 1.015^‡ 1.014^‡ 1.003

∆ ˆF4 0.999 0.963 0.987 0.977 1.015^†

∆ ˆF5 1.017^‡ 1.003 1.010 1.004 0.999

∆ ˆF1, ∆ ˆF4 1.007 0.956 1.001 0.982 1.016^‡

∆ ˆF1, ∆ ˆF5 1.017^∗ 0.977 1.037^† 1.023^‡ 1.002

∆ ˆF1, ∆ ˆF4, ∆ ˆF5 1.015^∗ 0.959 1.030^∗ 0.992 1.014^† Rolling Window Method: Autoregressive Benchmark

Factors j= 1 j= 3 j= 6 j= 9 j= 12

∆ ˆF1 1.020^∗ 0.981 1.028^‡ 1.015^† 0.998

∆ ˆF4 0.992 0.962 0.979 0.997 0.994

∆ ˆF5 1.009^‡ 0.986 1.027^† 0.993 1.001

∆ ˆF1, ∆ ˆF4 1.007 0.962 0.999 1.009^∗ 0.998

∆ ˆF1, ∆ ˆF5 1.027^† 0.967 1.069^‡ 1.012^† 0.998

∆ ˆF1, ∆ ˆF4, ∆ ˆF5 1.013^∗ 0.950^† 1.040^† 1.014^† 0.997

Note: We report the RRMSPE, the root mean squared prediction error from the benchmark model relative to that of our factor model. TheRRMSPE in bold indicates that it is greater than one, which implies that our factor model performs better than the benchmark model. *,

†, and‡ denote a rejection of the equal predictability of the DMW test statistics at the 10%, 5%, and 1%, respectively. We use the asymptotic critical values for the test with the random walk benchmark, whereas critical values from McCracken (2007) were used for the test with the AR benchmark. The DMW statistics are omitted to save space, but are available upon request from authors.